On an obstruction for perfect matchings

Abstract

Steffens [3] introduced a substructure (called below a “compressed set”) which prevents a graph from having a perfect matching, and proved that a countable graph possesses a perfect matching if and only if it does not contain such a substructure. In this paper we study some properties of compressed sets.

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References

  1. [1]

    R. Aharoni, On the equivalence of two conditions for the existence of transversals,J. Comb. Th. Ser. A.,34 (1983), 202–214.

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    R. Aharoni, Matchings in graphs of size ℵ1, submitted for publication.

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    K. Steffens, Matchings in countable graphs,Can. J. Math. 29 (1976), 165–168.

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Dedicated to Paul Erdős on his seventieth birthday

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Aharoni, R. On an obstruction for perfect matchings. Combinatorica 4, 1–6 (1984). https://doi.org/10.1007/BF02579151

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AMS subject classification (1980)

  • 04 A 20
  • 03 E 05